Timeline for Has this generalization of a determinant (assigning multiplicities to the rows) been studied?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
|
|
| Apr 9, 2014 at 21:43 | vote | accept | Drew | ||
| Jan 9, 2014 at 5:53 | comment | added | Victor Protsak | Also, a less philosophical comment regarding the $m\times n$ matrix $A$ versus a square matrix $\widehat{A}$ with repeated rows. The determinant is exceptional in that its value on a matrix with repeating rows vanishes. Thus a determinant minor vanishes if the row indices repeat. However, this is not so for the permanent and similar expressions. In particular, it's perfectly fine classically to talk about a permanent minor of order $n$ of an $m\times n$ matrix, where the row indices include some repetitions (or multiplicities). | |
| Jan 9, 2014 at 5:46 | comment | added | Victor Protsak | You are welcome, Drew! Without enough background knowledge, I can't be sure, but here are 2 things to keep in mind re your original motivation. Firstly, it's just possible that the appropriate de-tropicalization of the "determinant with multiplicities" is not the usual determinant - for example, it may be an immanant-like expression where the coefficients are not prescribed in advance (they may be generic variables). And secondly, not everything generalizes and it may sometimes be necessary to work out completely new proofs in your context rather than trying to imitate existing ones. | |
| Jan 8, 2014 at 16:04 | comment | added | Drew | Thank you for your response-- I had not seen immanants before. Indeed my original motivation is from repeated rows-- I edited my question to include that. | |
| Jan 8, 2014 at 6:43 | history | edited | Victor Protsak | CC BY-SA 3.0 |
added a speculative determinant-like expression, copyedited
|
| Jan 8, 2014 at 1:39 | history | answered | Victor Protsak | CC BY-SA 3.0 |